Spring Final Flashcards
Arithmetic Sequence
A sequence in which the difference of consecutive terms is constant
Asymptote
A line that a graph approaches more and more closely
Change of base formula
A formula that allows you to rewrite a logarithm in terms of logs written with another base
Circle
A round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center)
Combined Variation
A situation where a variable depends on other variables, and varies directly or inversely
Common Difference
The constant difference (d) between consecutive terms of an arithmetic sequence
Common Logarithm
A logarithm with base 10, denoted as log10, or simply just log
Common Ratio
The constant ratio (r) between consecutive terms of a geometric sequence
Completing the Square
To add a term (c) to an expression of the form x^2 + bx such that x^2 + bx + c is a perfect square trinomial
Complex Conjugates
Pairs of complex numbers of the forms a + bi and a - bi, where b does not equal 0
Complex Fraction
A fraction that contains a fraction in its numerator or denominator
Complex Number
A number written in the form a + bi, where a and b are real numbers
Composition of Functions
Operations that can be performed with 2 functions
Compound Inequality
2 inequality statements that are joined either by the word ¨or¨ or by the word ¨and¨ (¨and¨ would mean both statements are true).
Conic Section
A curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse
Consistent
If a liner or nonlinear system of equations has at least one set of values that satisfies each equation in the system, it is consistent (substituted into each equation while it still holds true as an identity)
Constant of Variation
The constant (a) in the inverse variation equation y = a/x, where a does not equal 0
Continuous Relation
A set of input values that consists of all numbers in an interval
Correlation Coefficient
A number (r) from -1 to 1 that measures how well a line fits a set of data pairs (x,y)
Dependent
Depends on the value of another number
Dimensions of a matrix
The dimensions of a matrix with (m) rows and (n) columns are m x n (read ¨m by n¨)
Direct Variation
Mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other
Discriminant
A parameter of an object or system calculated as an aid to its classification or solution. Also are defined for elliptic curves, finite field extensions, quadratic forms, and other mathematical entities
Ellipse
a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant, or resulting when a cone is cut by an oblique plane which does not intersect the base
End Behavior
The behavior of the graph of a function as x approaches positive infinity or negative infinity
Exponential Equation
An equation in which variable expressions occur as exponents
Extraneous Solution
A solution that is not a solution of the original equation
Extrema
Any point at which the value of a function is smallest or largest
Factor Theorem
A theorem linking factors and zeroes of a polynomial
Finite Sequence
A list of terms in a specific order. The sequence has a first term and a last term. The order of the terms follows some type of mathematical pattern or logical arrangement.
Function
An equation for which any x that can be plugged into the equation will yield exactly one y out of the equation; a special relationship where each input has a single output, and x is often the input value
Geometric Sequence
A sequence in which the ratio of any term to the previous term is constant
Greatest integer function
Also called step function, this is a piecewise function whose graph looks like the steps of a staircase. It is denoted by f(x) = [x] and is defined as the greatest integer less or equal to x.
Growth Factor
The value of b in an exponential growth function of the form y = ab^x, where a > 0 and b > 1
Hyberbola
A special arch-shaped curve that follows these rules
for any point, the distances:
from that point to a fixed point (the focus), and
from that point to a fixed straight line (the directrix)
are always in the same ratio.
It is one of the “Conic Sections”
Identity Function
Also called an identity relation or identity map or identity transformation, it is a function that always returns the same value that was used as its argument. That is, for f being identity, the equality f(x) = x holds for all x.
Imaginary unit
The square root of -1, denoted i = the square root of -1
Inconsistent
When a system has no solution, and the lines on the graphs do not intersect
Independent
A variable in an equation that may have its value chosen freely without considering the values of other variables
Infinite Sequence
An endless progression of numbers, which may include all the numbers of a particular set, or could be an arithmetic of geometric sequence
Interval notation
A way to describe continuous sets of real numbers by the numbers that bound them. Meant to denote a specific point
Inverse Functions
Functions that undo each other
Inverse Relation
The set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function. If the graph of a function contains a point (a, b), then the graph of the inverse relation of this function contains the point (b, a).
Inverse Variation
Two variables x and y show this when y = a/x, where a is not equal to 0
Joint Variation
when a variable varies directly or inversely with multiple variables. For instance, if x varies directly with both y and z, we have x = kyz
Latus rectum
The latus rectum of a conic section is the chord through a focus parallel to the conic section directrix
Linear programming
A method of optimizing operations with some constraints. The main objective is to maximize or minimize the numerical value.
Logarithm
a quantity representing the power to which a fixed number (the base) must be raised to produce a given number
Logistic growth model
biological population with plenty of food, space to grow, and no threat from predators, tends to grow at a rate that is proportional to the population – that is, in each unit of time, a certain percentage of the individuals produce new individuals
Matrix
a collection of numbers arranged into a fixed number of rows and columns
nth root
used n times in a multiplication to get the original value. It is the general way of talking about roots
Natural Logarithm
a number´s logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately equal to 2.718281828459
Negative Exponent
how many times to divide the number by
Parabola
a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves
Parent Function
the simplest function of a family of functions that preserves the definition (or shape) of the entire family
Piecewise defined function
a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain, and expresses the function rather than a characteristic of it in itself
Point-slope form
the equation of a straight line in the form y − y1 = m(x − x1) where m is the slope of the line and (x1, y1) are the coordinates of a given point on the line
Quadratic Function
a function that can be described by an equation of the form fx = ax2 + bx + c, where a ≠ 0
Radicand
The value inside the radical symbol
Rate of change
used to mathematically describe the percentage chance in a value over a defined period of time
Rational exponent
An exponent that is also a fraction
Rational function
any function which can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials
Rationalizing the denominator
to eliminate any radical expressions in the denominator such as square roots and cube roots. The key idea is to multiply the original fraction by an appropriate value, such that after simplification, the denominator no longer contains radicals
Recursive formula
a formula that defines each term of a sequence using preceding term(s). Recursive formulas must always state the initial term, or terms, of the sequence
Regression Line
an estimate of the line that describes the true, but unknown, linear relationship between the two variables. The equation of the regression line is used to predict (or estimate) the value of the response variable from a given value of the explanatory variable
Relative maximum
a point that is higher than the points directly beside it on both sides
Relative minimum
a point that is lower than the points directly beside it on both sides
Root
Where a function equals 0
Scatter Plot
A graph of plotted points that show the relationship between two sets of data
Sequence
an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members
Set-builder notation
a shorthand used to write sets, often for sets with an infinite number of elements. It is used with common types of numbers, such as integers, real numbers, and natural numbers. This notation can also be used to express sets with an interval or an equation
Step function
a function on the real numbers is this if it can be written as a finite linear combination of indicator functions of intervals
Synthetic Division
a simplified method for dividing a polynomial by another polynomial of the first degree by writing down only the coefficients of the several powers of the variable and changing the sign of the constant term in the divisor so as to replace the usual subtractions by additions
Vertex Form
the alternate way of writing out a parabola for an equation
Vertical line test
a visual way to determine if a curve is a graph of a function or not
Zeros
When a function equals the value 0
